A Unified Approach to Generalized Stirling Functions

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Abstract

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in \cite{He11}. Previous well-known Stirling functions introduced by Butzer and Hauss \cite{BH93}, Butzer, Kilbas, and Trujilloet \cite{BKT03} and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in \cite{HS98} to the defined Stirling functions.

Original languageAmerican English
JournalJournal of Mathematical Research with Applications
StatePublished - Oct 2012

Keywords

  • Stirling numbers
  • Stirling functions
  • factorial polynomials
  • generalized factorial
  • divided difference
  • $k$-Gamma functions
  • Pochhammer symbol and $k$-Pochhammer symbol.

Disciplines

  • Applied Mathematics
  • Mathematics

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